Question: Simplify the following expression: $y = \dfrac{z^2 - 3z - 40}{z - 8} $
Explanation: First factor the polynomial in the numerator. $ z^2 - 3z - 40 = (z - 8)(z + 5) $ So we can rewrite the expression as: $y = \dfrac{(z - 8)(z + 5)}{z - 8} $ We can divide the numerator and denominator by $(z - 8)$ on condition that $z \neq 8$ Therefore $y = z + 5; z \neq 8$